Effective interactions and superconductivity in the t-J model in the large-N limit

TL;DR

This paper develops a perturbation expansion for the t-J model using X-operators, deriving a linearized equation for superconductivity, and finds a d-wave pairing instability with doping-dependent transition temperatures.

Contribution

It introduces a perturbation expansion for the t-J model with X-operators and derives a linearized superconducting gap equation in the large-N limit.

Findings

Superconducting instability occurs for even frequency d-wave pairing.

Transition temperature varies with doping levels.

Effective interaction strength depends on doping.

Abstract

The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym- Kadanoff functional method. As an application we derive explicit expressions for the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice. We find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike symmetry. Results for the transition temperature and the effective interaction are given as a function of doping.